Chalice makes use of access predicates to achieve what separation logic uses separating conjunction as. The condition you wrote above says nothing about whether or not c1 and c2 are equal (well, actually it does, since you equated the two respective
x fields with 1 and 2; this implies that c1 and c2 are different).

If you want to say that c1.x and c2.x live in separate heaps, you would write: acc(c1.x) && acc(c2.x). Roughly speaking, you can think of && in Chalice as separating conjunction and think of the separation-logic "points to" relation

c.x |-> _

as acc(c.x).

Chalice "evaluates" (that is, interprets) expressions use the two semantic transformations "inhale" and "exhale". I refer you to the paper: "A basis for verifying multi-threaded programs" by Leino and Müller, ESOP 2009. For more of
a comparison between Chalice and separation logic, I refer you to "Relationship between Separation Logic and Implicit Dynamic Frames" by Parkinson and Summers, ESOP 2011.

There is only one heap, just like there's just one heap when the program executes. But an activation record (like a method) only has access to certain parts of the heap. Access to the heap is tracked by the Mask (which I think Peter and I wrote
as a caligraphic P in our paper).

What does "holding in separate heaps" really mean? It means that you could partition the memory in such a way that the two memory locations (in your example, c1.x and c2.x) are placed in different partitions. The inhale and exhale operations,
which operate on the Mask, make sure of that. But the values stored in the various memory locations are all modeled in the Boogie variable called Heap.

Again, Peter's and my ESOP 2009 paper attempts to describes these things. In Chalice, you don't really think of things as being "separate heaps", even though you can take that viewpoint as well. To get the usual Chalice mindset, I recommend the
Chalice tutorial: "Verification of concurrent programs in Chalice", by Leino, Müller, and Smans (lecture notes from FOSAD 2009). You can find it from the Chalice page,
http://research.microsoft.com/en-us/projects/chalice/.